Tony Pulis is an MOT tester in the luxury showroom of the Premier League. His approach to away matches boils down to checking whether others' fancy fleets meet minimum requirements. Can opponents run, jump, jostle and scrap? If so, they are roadworthy. And will probably win at home to Stoke, who, on their travels, tend to expose anyone who fails to do the basics and lose to anyone who satisfies that low standard.

They have never got so much as a point at the Emirates but Arsène Wenger's team have been humbled at home so many times this season that the visit of Inspector Pulis was seen as a significant test of Arsenal's Champions League qualification credentials.

Now, after a victory secured by a deflected free-kick from Lukas Podolski in the 78th minute, we have proof that Arsenal can consistently run, jump, jostle and scrap for 90 minutes. We also know that Wenger, often depicted as having become too aloof or idealistic to concentrate on such vulgar aspects of the game, can still set a side up to do just that. For the visit of Stoke he dropped the silky Santi Cazorla and instructed Abou Diaby to serve as a shield in front of the back four, who were ordered to dominate the airways around Peter Crouch.

Abou Diaby, right, battles with Stoke's Geoff Cameron after he was drafted in to add some steel to Arsenal's midfield. Photograph: Kerim Okten/EPA

Diaby, Jack Wilshere and Mikel Arteta never shirked a tackle in midfield and Olivier Giroud more than held his own in the air against the twin colossi of Robert Huth and Ryan Shawcross. Once they had got those fundamentals right, only one team looked incisive and ambitious enough to achieve victory.

"I think it is more mental preparation," Wenger said. "You tell your central defenders you have to be ready and they [Stoke] are good on the second ball too, so your midfielders have to be good on the second ball, to fight for it and let you play your game.

"We played Diaby because in front of the defence he can win some headers. In England you have to cope with all kinds of football without losing the quality you want to play and that is not always easy because if you have 10 Cazorlas, you would have a very good technical team but against Stoke you would struggle."

Wenger could take particular satisfaction from the performance of Nacho Monreal, the left-back he signed from Málaga on transfer deadline day to replace the injured Kieran Gibbs. There must have been a fear that a player who has spent his whole career in La Liga might struggle to adapt to the in-your-face crudeness of Stoke's approach but the 26-year-old was willing and able to compete physically with Jonathan Walters and also showed deftness and enterprise going forward. More attack-minded visitors will seek to put more sustained pressure on Arsenal's defenders but here Monreal looked a valuable addition.

The club's fans would undoubtedly have liked Wenger to make even more such additions in January and the manager again insisted that it was impossible to find other players of sufficient quality and said he should be praised for at least capturing Monreal. "I found at least one, you have to give me at least that credit," he said. "I would have loved to take somebody else but we didn't find. We worked very hard on it, we were everywhere. In the Africa Cup of Nations, the best player is Gervinho and we already have Gervinho. It is very difficult for top clubs to find someone in the middle of the season."

A statistic that shows how loose Arsenal's grip has become this season on top-club status is that this was only their fourth win from 13 matches against teams in the top half of the Premier League. That is why they are at risk of missing out on the Champions League for the first time in 15 seasons. The flawless record of reaching that tournament is the main achievement that Wenger can still point to with pride when people complain about the absence of trophies since 2005. His team showed they are ready to fight to uphold it and on a weekend when Chelsea unravelled and Everton slipped up at home, that can only encourage Wenger. Pulis, meanwhile, could do with reviewing Stoke's road worthiness on the road.